Events A and B are not independent because [tex]P(A / B) \neq P(A)[/tex]
Step-by-step explanation:
Given that [tex]P(A)=0.25[/tex], [tex]P(B)=0.3[/tex] and [tex]P(A \text { and } B)=0.05[/tex]
Two events are said to be independent events, if it satisfies any one of the following conditions,
[tex]P(A / B) = P(A)[/tex] or [tex]P(B / A) = P(B)[/tex] or [tex]P(AB)=P(A)P(B)[/tex]
First, let us substitute the values in the equation [tex]P(A / B) = P(A)[/tex]
The formula to find [tex]P(A / B)[/tex] is [tex]P(A / B)=\frac{P(A \cap B)}{P(B)}[/tex]
Substituting the values, we get,
[tex]P(A / B)=\frac{0.05}{0.3} =0.1667[/tex]
But [tex]P(A)=0.25[/tex]
Hence, [tex]P(A / B) \neq P(A)[/tex]
Thus, A and B are not independent events.
